How to animate assembly of DNA bases?
Here is a way to do it, a bit tedious because you have a lot of duplications and NLA strips to move but it works.
Basically the method is to create 3 linked-duplicated bars, create an action for each one that makes it stick to the vertical bars, push these actions into the NLA, link-duplicate these 3 different bars and, in the NLA, move the strips so that it delays the animation for each one.

Create the path, create one vertical bar, give it a Follow Path constraint with the path as Target, click on Animate Path.
Link-duplicate the bar (AltD), in the Follow Path constraint change its Offset so that it's a bit in front of the first one. Repeat until you have a lot of bars.



Create a second bar, put it somewhere above the path, where it can't be seen by your camera at the beginning of its animation, animate it so that at one key moment it sticks to the vertical bar. Then create a last keyframe so that it keeps sticking to the vertical bar until the end of the animation, for this last part make sure that the animation is linear (in the Dope Sheet select the keyframes and press T &gt; Linear)



In the Dope Sheet, press Push Down in order to push the animation into the NLA.
Link-duplicate this second bar, in the NLA, move the second bar's strip so that it sticks perfectly to another vertical bar:



Link-duplicate the bar, create a second animation in the Dope Sheet that makes it stick to the second vertical bar, push the action in the NLA:



Then same thing, link-duplicate this bar, in the NLA move the strip so that it makes it sticks to another vertical bar, and so on: